Geodesic
Hamiltonians associated with the~sixth Painlev\'e equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 54-65

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We obtain the formula determining the general form of polynomial Hamiltonians associated with the sixth Painlevé equation and prove its uniqueness. We prove the existence of nonpolynomial Hamiltonians associated with this equation. We identify the Hamiltonian class for which the defining differential equation coincides with the equation ($h$-equation) for the simplest polynomial Hamiltonian (the Okamoto Hamiltonian).
Keywords: Painlevé equation, Hamiltonian, family of solutions, Bäcklund transformation
Mots-clés : Heun equation. 
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     author = {V. V. Tsegel'nik},
     title = {Hamiltonians associated with the~sixth {Painlev\'e} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {54--65},
     publisher = {mathdoc},
     volume = {151},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a3/}
}
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V. V. Tsegel'nik. Hamiltonians associated with the~sixth Painlev\'e equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 54-65. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a3/